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Oscillatory flow regimes for a circular cylinder near a plane boundary

Published online by Cambridge University Press:  04 April 2018

Chengwang Xiong Open the ORCID record for Chengwang Xiong [Opens in a new window] ,
Liang Cheng ,
Feifei Tong  and
Hongwei An Open the ORCID record for Hongwei An [Opens in a new window]
Chengwang Xiong
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia School of Civil Engineering, Hebei University of Technology, Tianjin, 300401, China
Liang Cheng*
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia DUT-UWA Joint Research Centre, State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian 116024, China
Feifei Tong
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Hongwei An
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
*
†Email address for correspondence: liang.cheng@uwa.edu.au
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Abstract

Oscillatory flow around a circular cylinder close to a plane boundary is numerically investigated at low-to-intermediate Keulegan–Carpenter ($KC$) and Stokes numbers ($\unicode[STIX]{x1D6FD}$) for different gap-to-diameter ratios ($e/D$). A set of unique flow regimes is observed and classified based on the established nomenclature in the ($KC,\unicode[STIX]{x1D6FD}$)-space. It is found that the flow is not only influenced by $e/D$ but also by the ratio of the thickness of the Stokes boundary layer ($\unicode[STIX]{x1D6FF}$) to the gap size (e). At relatively large $\unicode[STIX]{x1D6FF}/e$ values, vortex shedding through the gap is suppressed and vortices are only shed from the top of the cylinder. At intermediate values of $\unicode[STIX]{x1D6FF}/e$, flow through the gap is enhanced, resulting in horizontal gap vortex shedding. As $\unicode[STIX]{x1D6FF}/e$ is further reduced below a critical value, the influence of $\unicode[STIX]{x1D6FF}/e$ becomes negligible and the flow is largely dependent on $e/D$. A hysteresis phenomenon is observed for the transitions in the flow regime. The physical mechanisms responsible for the hysteresis and the variation of marginal stability curves with $e/D$ are explored at $KC=6$ through specifically designed numerical simulations. The Stokes boundary layer over the plane boundary is found to be responsible for the relatively large hysteresis range over $0.25<e/D<1.0$. Three mechanisms have been identified to the change of the marginal stability curve over $e/D$, which are the blockage effect due to the geometry setting, the favourable pressure gradient over the gap and the location of the leading eigenmode relative to the cylinder.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 127 - 161
Copyright
© 2018 Cambridge University Press 

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Xiong et al. supplementary movie 1

Animation of streakline in regime HA at (e/D, KC, β)=(0.25,10, 10).

Download Xiong et al. supplementary movie 1(Video)
Video 5.6 MB

Xiong et al. supplementary movie 2

Animation of streakline in regime GVS at (e/D, KC, β)=(0.5, 6, 20).

Download Xiong et al. supplementary movie 2(Video)
Video 3.3 MB

Xiong et al. supplementary movie 3

Animation of streakline in regime GVS-A at (e/D, KC, β)=(0.5, 6, 30).

Download Xiong et al. supplementary movie 3(Video)
Video 3.2 MB

Xiong et al. supplementary movie 4

Animation of streakline in regime E at (e/D, KC, β)=(2, 6, 30).

Download Xiong et al. supplementary movie 4(Video)
Video 3.3 MB

Xiong et al. supplementary movie 5

Animation of streakline in regime F' at (e/D, KC, β)=(0.25, 11, 20).

Download Xiong et al. supplementary movie 5(Video)
Video 4.3 MB

Xiong et al. supplementary movie 6

Animation of streakline in regime F at (e/D, KC, β)=(2, 10, 20).

Download Xiong et al. supplementary movie 6(Video)
Video 7 MB